1. Field of the Invention
The present invention relates to an incoming direction estimation apparatus.
2. Description of the Related Arts
FIG. 1 is a diagram showing a mono-pulse radar as an example of a conventional incoming direction estimation apparatus.
This apparatus is a system comprising one transmission antenna AT, two reception antennas AR0 and AR1, an interface module (this comprisal adopts a single-pole, double-throw (SPDT)), which interfaces the reception antennas, and a radio frequency (RF) unit, an RF unit constituted by a transceiver and receiver, an RF oscillator, a base band (BB) oscillator, a BB module (not shown herein) comprising an analog to digital (A/D) converter, et cetera, and a signal processing apparatus (also not shown herein) comprising a central processing unit (CPU) and such. A radar wave transmitted from the antenna AT is received by the antennas AR0 and AR1 after being reflected on an angle measurement target. The radar wave transmitted from the antenna AT uses an RF signal that is a resultant of an oscillation frequency of the RF oscillator RF-VCO being modified by a signal of a triangular wave oscillated and emitted by the base band oscillator BB-OSC, or the like wave, followed by being amplified by a high power amplifier (HPA). The radar wave received by the antennas AR0 and AR1 is led by way of the switch SPDT, amplified by the low noise amplifier (LNA), mixed with the transmission radar wave by the multiplier M and converted into a base band signal BB. Thus obtained base band signal BB is processed by the BB module and CPU that are placed in the later stage, and an incoming direction of the radar wave (named simply as “radar wave” hereinafter) reflected on the angle measurement target is estimated.
Assuming that the angle measurement target is positioned at an angle θ relative to the normal line direction of the antenna surface (angle measurements are made clockwise with illustrated normal line as 0 degrees), a signal x(t) incoming from the target at a clock time t is received by the antennas AR0 and AR1, and down-converted, thereby becoming a base band signals y0(t) and y1(t) as the following expressions:y0=x+n0  (1.1)y1=xexp[j2πα sin θ]+n1  (1.2);
where n0(t) and n1(t) are noise components and t is omitted for simplicity of an expression; and α is d/λ assuming that the antenna interval is d, the wavelength of an un-modulated output signal (named as “carrier signal” hereinafter) from the RF-VCO is λ, and j is an imaginary unit. In this case, the simplest method for calculating the θ among conceivable methods is definingΣy≡y0+y1,Δy≡y0−y1,Σn≡n0+n1, andΔn≡n0−n1  (1.3)
followed by calculating a ratio of Δy to Σy to obtain:
                                                                                          Δ                  ⁢                                                                          ⁢                  y                                                  Σ                  ⁢                                                                          ⁢                  y                                            =                                                                    x                    ⁢                                          {                                              1                        -                                                  exp                          ⁡                                                      [                                                          j                              ⁢                                                                                                                          ⁢                              2                              ⁢                              π                              ⁢                                                                                                                          ⁢                              α                              ⁢                                                                                                                          ⁢                              sin                              ⁢                                                                                                                          ⁢                              θ                                                        ]                                                                                              }                                                        +                                      n                    0                                    -                                      n                    1                                                                                        x                    ⁢                                          {                                              1                        +                                                  exp                          ⁡                                                      [                                                          j2πα                              ⁢                                                                                                                          ⁢                              sin                              ⁢                                                                                                                          ⁢                              θ                                                        ]                                                                                              }                                                        +                                      n                    0                                    +                                      n                    1                                                                                                                          =                                                                                          -                      2                                        ⁢                    j                    ⁢                                                                                  ⁢                    x                    ⁢                                                                                  ⁢                                          sin                      ⁡                                              [                                                  πα                          ⁢                                                                                                          ⁢                          sin                          ⁢                                                                                                          ⁢                          θ                                                ]                                                              ⁢                                          exp                      ⁡                                              [                                                  jπα                          ⁢                                                                                                          ⁢                          sin                          ⁢                                                                                                          ⁢                          θ                                                ]                                                                              +                                      Δ                    ⁢                                                                                  ⁢                    n                                                                                        2                    ⁢                    x                    ⁢                                                                                  ⁢                                          cos                      ⁡                                              [                                                  πα                          ⁢                                                                                                          ⁢                          sin                          ⁢                                                                                                          ⁢                          θ                                                ]                                                              ⁢                                          exp                      ⁡                                              [                                                  jπα                          ⁢                                                                                                          ⁢                          sin                          ⁢                                                                                                          ⁢                          θ                                                ]                                                                              +                                      Σ                    ⁢                                                                                  ⁢                    n                                                                                                                                          =                                                                                                    -                        j                                            ⁢                                                                                          ⁢                                              tan                        ⁡                                                  [                                                      πα                            ⁢                                                                                                                  ⁢                            sin                            ⁢                                                                                                                  ⁢                            θ                                                    ]                                                                                      +                    Σɛ                                                        1                    +                    Σɛ                                                              ;                                                          (        1.4        )            
and therefore the θ can be calculated by using the following expression provided that Δε and Σε are sufficiently small.
                              θ          ≈                                    sin                              -                1                                      ⁢                          {                                                1                  πα                                ⁢                                                      tan                                          -                      1                                                        ⁡                                      [                                          -                                              Im                        ⁡                                                  (                                                                                    Δ                              ⁢                                                                                                                          ⁢                              y                                                                                      Σ                              ⁢                                                                                                                          ⁢                              y                                                                                )                                                                                      ]                                                              }                                      ;                            (        1.5        )            
where the following is defined:
                                          Σɛ            ≡                                          Σ                ⁢                                                                  ⁢                n                                            2                ⁢                x                ⁢                                                                  ⁢                                  cos                  ⁡                                      [                                          πα                      ⁢                                                                                          ⁢                      sin                      ⁢                                                                                          ⁢                      θ                                        ]                                                  ⁢                                  exp                  ⁡                                      [                                          jπα                      ⁢                                                                                          ⁢                      sin                      ⁢                                                                                          ⁢                      θ                                        ]                                                                                =                                    Σ              ⁢                                                          ⁢              n                                                      Σ                ⁢                                                                  ⁢                y                            -                              Σ                ⁢                                                                  ⁢                n                                                    ,                                  ⁢        and                            (        1.6        )                                          Δɛ          ≡                                    Δ              ⁢                                                          ⁢              n                                      2              ⁢              x              ⁢                                                          ⁢                              cos                ⁡                                  [                                      πα                    ⁢                                                                                  ⁢                    sin                    ⁢                                                                                  ⁢                    θ                                    ]                                            ⁢                              exp                ⁡                                  [                                      jπα                    ⁢                                                                                  ⁢                    sin                    ⁢                                                                                  ⁢                    θ                                    ]                                                                    =                              Δ            ⁢                                                  ⁢            n                                Σ            ⁢                                                  ⁢            y            ⁢                                                  ⁢            Σ            ⁢                                                  ⁢            n                                              (        1.7        )            
Note that Im takes an imaginary number part of an argument in the above expression. Now, let it be assumed that γ is expressed by γ=−Im(Δy/Σy), then it is necessary to set it at α=1/2 in order to be able to use the entirety of a domain of sin−1 (where sin−1(x); |x|≦1) if tan−1(γ) changes when trying to obtain a maximum field of view (FOV) (i.e., a field angle of a radar) because the value range of the tan−1(γ) determining the domain of definition of sin−1 is |tan−1(γ)|≦π/2. It is, however, difficult to set the α at such a value because of a consideration of a system gain and an electromagnetic coupling between the antennas, and therefore the α is usually set at about 1 to 2. That is, α=d/λ where the antenna interval is d and a wavelength of the carrier signal is λ, and therefore the antennas must be placed in an extremely small interval in the unit of millimeter in order to accomplish a value such as α=1/2 by a short wave signal especially a radar or such. Too small an antenna interval, however, generates an electromagnetic coupling between the two antennas, losing an independence of two reception signals that are supposed to be obtained by essentially maintaining an exact phase difference indicated by the above expressions 1.1 and 1.2, and therefore an approximation represented by the expression 1.5 is no longer applicable even if Δy/Σy is forcibly transformed, resulting in making it difficult to estimate the θ accurately. Meanwhile, a try to obtain a sufficient system gain needs to take a sufficient gain of the antennas, generally requiring a large area size for each antenna. Consequently, a try to obtain a sufficient system gain makes the antennas become large, creating a situation of making it impossible to minimize the antenna interval.
Accordingly, one considers a way of obtaining a maximum FOV based on such an α (e.g., FOV≈±23° in the case of α=1.25), in which case, however, an angle must be measured by using the entire value zone of tan−1(γ). The tan−1(γ), however, is a nonlinear function in which a derivative becomes smaller than “1” with a distance from the original point, and the nonlinearity of the tan−1(γ) further influences the sin−1 that is also a nonlinear function adversely to a large γ (i.e., to a signal incoming from an angle close to an FOV limit), thus resulting in fundamentally degrading accuracy of a measurement angle.
Incidentally, there is a known technique (per reference patent documents 1 and 2) of configuring an array by placing three element antennas in irregular intervals, carrying out a conventional mono-pulse angle measurement by using two sets of antennas, and applying an averaging operation and such, in order to reduce an error nearby the FOV. Except that the error reduction method of the known technique is an extension of the conventional mono-pulse method using two signals after all.
In summary, the conventional incoming direction estimation apparatus has been faced with the following problems:
1. A mono-pulse apparatus employing two reception-use sensors are commonly used for an apparatus estimating a direction of arrival (DOA) of a single signal by using a signal sensor comprising a sensor array. The apparatus, however, has a limited field of view (FOV) constrained by an absolute interval between the sensors and, moreover, a direction estimation error increases toward the edges of the FOV in terms of the primary value of an inverse triangular function. Meanwhile, a try to increase the FOV is limited by a difficulty of setting individual sensors less than a certain interval due to the problem of physical size, gain or electromagnetic coupling of the individual sensors.
2. There is a known technique (per reference patent documents 1 and 2) as a proposal for correcting a DOA error nearby the FOV among the problems noted in the above paragraph 1. These apparatuses place three or more antennas in irregular intervals, configures two sets of common mono-pulse apparatuses by selecting two antennas among the three or more antennas, applies to averaging or such to two DOAs θ0 and θ1 that are obtained from each mono-pulse apparatus and judges that a correct DOA is obtained only if the both of them are identical. In this method, however, the FOV per se is still controlled by the absolute interval between the antennas, thus failing to provide a fundamental solution to the problem of the above paragraph 1. Another problem is that an essential degradation of an accuracy of measurement angle cannot be avoided because it is basically a simple combination of two sets of conventional mono-pulse apparatuses.
Patent document 1: Japanese Patent Application No. 2004-228615
Patent document 2: Laid-Open Japanese Patent Application Publication No. 2000-230974